Quasi-abelian hearts of twin cotorsion pairs on triangulated categories

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Abstract

We prove that, under a mild assumption, the heart H‾ of a twin cotorsion pair ((S,T),(U,V)) on a triangulated category C is a quasi-abelian category. If C is also Krull-Schmidt and T=U, we show that the heart of the cotorsion pair (S,T) is equivalent to the Gabriel-Zisman localisation of H‾ at the class of its regular morphisms. In particular, suppose C is a cluster category with a rigid object R and [XR] the ideal of morphisms factoring through XR=Ker(HomC(R,−)), then applications of our results show that C/[XR] is a quasi-abelian category. We also obtain a new proof of an equivalence between the localisation of this category at its class of regular morphisms and a certain subfactor category of C.

OriginalsprogEngelsk
TidsskriftJournal of Algebra
Vol/bind534
Sider (fra-til)313-338
Antal sider26
ISSN0021-8693
DOI
StatusUdgivet - 15 sep. 2019
Udgivet eksterntJa

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